Topological Trajectory Classification with Filtrations of Simplicial Complexes and Persistent Homology

Florian T. Pokorny, Majd Hawasly, Subramanian Ramamoorthy
In International Journal of Robotics Research (IJRR), 2016


In this work, we present a sampling-based approach to tra- For robots to autonomously operate in a wide variety of jectory classification which enables automated high-level reasoning about topological classes of trajectories. Our approach is applicable to general configuration spaces and relies only on the availability of collision free samples. Unlike previous sampling-based approaches in robotics which use graphs to capture information about the path-connectedness of a configuration space, we construct a mul- tiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classifi- cation. We propose a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension and for sets of trajectories starting and ending in two fixed points. Using a cone construction, we then generalize this approach to classify sets of trajectories even when trajectory start and end points are allowed to vary in path-connected subsets. We furthermore show how an augmented filtration of simplicial complexes based on an arbitrary function on the configuration space, such as a costmap, can be defined to incorporate additional constraints. We present an evaluation of our approach in 2, 3, 4 and 6 dimensional configuration spaces in simulation and in real-world experiments using a Baxter robot and motion capture data.


@article{pokorny2016c, author = {Pokorny, Florian T. and Hawasly, Majd and Ramamoorthy, Subramanian}, title = {Topological Trajectory Classification with Filtrations of Simplicial Complexes and Persistent Homology}, journal = {International Journal of Robotics Research (IJRR)}, year = {2016}, }


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